Distributed Non-Uniform Scaling Control of Multi-Agent Formation via Matrix-Valued Constraints

2025-08-04

AI Summary

Existing distributed control approaches for multi-agent position-orientation coordinated formation support only isotropic scaling, failing to achieve anisotropic scaling along individual coordinate axes or concurrent orientation deformation. Method: This paper proposes a matrix-valued constraint-based local control protocol requiring only two leaders to adjust their positions, enabling globally convergent non-uniform scaling, translation, and orientation-preserving shape deformation over sparse bidirectional sensing graphs. Contribution/Results: We rigorously prove global asymptotic stability of the closed-loop system. Simulations demonstrate the method’s efficacy in executing complex formation transformations under low communication density. Compared with conventional affine control, our approach significantly enhances flexibility, scalability, and engineering practicability—particularly for heterogeneous agent networks with limited onboard computation and communication resources.

Technology Category

• Multiagent Systems: Coordination and Collaboration
• Intelligent Robots: Localization, Mapping, and Navigation
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Distributed formation maneuver control refers to the problem of maneuvering a group of agents to change their formation shape by adjusting the motions of partial agents, where the controller of each agent only requires local information measured from its neighbors. Although this problem has been extensively investigated, existing approaches are mostly limited to uniform scaling transformations. This article proposes a new type of local matrix-valued constraints, via which non-uniform scaling control of position formation can be achieved by tuning the positions of only two agents (i.e., leaders). Here, the non-uniform scaling transformation refers to scaling the position formation with different ratios along different orthogonal coordinate directions. Moreover, by defining scaling and translation of attitude formation, we propose a distributed control scheme for scaling and translation maneuver control of joint position-attitude formations. It is proven that the proposed controller achieves global convergence, provided that the sensing graph among agents is a 2-rooted bidirectional graph. Compared with the affine formation maneuver control approach, the proposed approach leverages a sparser sensing graph, requires fewer leaders, and additionally enables scaling transformations of the attitude formation. A simulation example is proposed to demonstrate our theoretical results.

Problem

• Achieve non-uniform scaling control in multi-agent formations
• Enable distributed control with only two leader agents
• Combine position-attitude formation scaling and translation

Innovation

• Matrix-valued constraints enable non-uniform scaling
• Two leaders control position-attitude formations
• Sparse sensing graph ensures global convergence